Aural pattern recognition experiments and the subregular hierarchy

Abstract We explore the formal foundations of recent studies comparing aural pattern recognition capabilities of populations of human and non-human animals. To date, these experiments have focused on the boundary between the Regular and Context-Free stringsets. We argue that experiments directed at distinguishing capabilities with respect to the Subregular Hierarchy, which subdivides the class of Regular stringsets, are likely to provide better evidence about the distinctions between the cognitive mechanisms of humans and those of other species. Moreover, the classes of the Subregular Hierarchy have the advantage of fully abstract descriptive (model-theoretic) characterizations in addition to characterizations in more familiar grammar- and automata-theoretic terms. Because the descriptive characterizations make no assumptions about implementation, they provide a sound basis for drawing conclusions about potential cognitive mechanisms from the experimental results. We review the Subregular Hierarchy and provide a concrete set of principles for the design and interpretation of these experiments. Keywords Sub-regular languages · Local languages · Artificial grammar learning · Cognitive complexity · Aural pattern recognition · Mathematics of language J. Rogers (B

The computational cost of generalizations: An example from micromorphology

Morphotactics has been argued to be limited to the formal class of tier-based strictly local languages (Aksënova et al., 2016). We claim that the level of the complexity of a pattern largely depends on the way it is morphologically analyzed. Using an example from adjectival inflection in Noon (Niger-Congo), we show that the complexity of this pattern falls in two different classes within the subregular hierarchy if viewed from different perspectives. In particular, the traditional segmentation of Noon affixes (Soukka 2000) yields a 3-TSL grammar, while the same pattern is 3-SSTSL under the perspective of micromorphology (Stump 2017). Both grammars require a locality window of 3 segments; however, the micromorphology-based analysis shows an increase in formal complexity, although it reduces the grammar size by defining complex affixes in terms of simpler ones

Learning Phonotactics in a Differentiable Framework of Subregular Languages

Phonotactic constraints have been argued to beregular, meaning that they can be represented usingfinite-state automata (Heinz, 2018); furthermore, they have been argued to occupy a even more restrictedregion of the regular language class known as the subregular hierarchy (Rogers & Pullum, 2011). Ourcontribution is to present a simple model of phonotactic learning from positive evidence. Our approach isbased on probabilistic finite-state automata (Vidal et al., 2005a,b). We study the model’s ability to induce localand nonlocal phonotactics from wordlist data, both with and without formal constraints on the automaton.In particular, we evaluate the ability of our learner to induce nonlocal phonotactic constraints from data ofNavajo and Quechua. Our work provides a framework in which different formal models of phonotactics canbe compared, and sheds light on the structural nature of phonological acquisition (Dai, 2021; Shibata & Heinz,2019; Heinz & Rogers, 2010, 2013)

Learning Nonlocal Phonotactics in a Strictly Piecewise Probabilistic Phonotactic Model

Phonotactic learning is a crucial aspect of phonological acquisition and has figured significantly in computational research in phonology (Prince & Tesar 2004). However, one persistent challenge for this line of research is inducing non-local co-occurrence patterns (Hayes & Wilson 2008). The current study develops a probabilistic phonotactic model based on the Strictly Piecewise class of subregular languages (Heinz 2010). The model successfully learns both segmental and featural representations, and correctly predicts the acceptabilities of the nonce forms in Quechua (Gouskova & Gallagher 2020)

Learning Local Phonological Processes

We present a learning algorithm for local phonological processes that relies on a restriction on the expressive power needed to compute phonological patterns that apply locally. Representing phonological processes as a functional mapping from an input to output form (an assumption compatible with either the SPE or OT formalism), the learner assumes the target process can be described with the functional counterpart to the Strictly Local (McNaughton and Papert 1971, Rogers and Pullum 2011) formal languages. Given a data set of input-output string pairs, the learner applies the two-stage grammatical induction procedure of 1) constructing a prefix tree representation of the input and 2) generalizing the pattern to words not found in the data set by merging states (Garcia and Vidal 1990, Oncina et al. 1993, Heinz 2007, 2009, de la Higuera 2010). The learner’s criterion for state merging enforces a locality requirement on the kind of function it can converge to and thereby directly reflects its own hypothesis space. We demonstrate with the example of German final devoicing, using a corpus of string pairs derived from the CELEX2 lemma corpus. The implications of our results include a proposal for how humans generalize to learn phonological patterns and a consequent explanation for why local phonological patterns have this property

from regular to strictly locally testable languages

Comment: In Proceedings WORDS 2011, arXiv:1108.341